What is the meaning of On-board clock set; was .... and why does it vary in advance and behind its respective ilo entry by exactly 1 hour. The linux system time (BST) has not changed in the same period...

The issue is related to how the Linux OS stores and reports the time, but stores GMT in the system RTC. You could expect this couple of events each time the system is reset and runs through post. (Unless your system happens to be located in the GMT zone :)

Windows OTOH, stores the local time in the system RTC, so the POST / OS load process does not normally perturb the iLO clock.